Envelope Function Theory Research Articles

Electronic structure and optical gain of InAsSbN/InAs quantum dots

The electronic structure and optical gain of InAsSbN/InAs QDs are investigated in the framework of effective-mass envelope function theory. The strain distribution is calculated using the valence force field (VFF) method. When the composition of Sb increases, both the conduction and valence bands offset and the compressive strain increase, and the transition energy decreases and the strained band alignment may change from type I to type II. The added nitrogen can reduce the compressive strain in QD, and it reduces the C1-HH1 transition energy due to the strong repulsion between nitrogen resonant band and conduction band. When the Sb composition increases, the overlapping of wave-functions of electrons and holes are less efficient, the optical transition matrix element decreases. For the optical gain, we should consider the factors including the transition matrix element, the matrix element of Kane’s theory, the refractive index and Fermi-Dirac distributions for electrons f c in the conduction bands and holes f v in the valence bands. So depending on the specific application requirements, we should select the appropriate compositions of Sb and N accordingly.

Calculation of valence band structures of InAs/GaAs quantum ring and quantum dot: using numerical Fourier transform method

This article puts forward a new method in calculating the band structures of low-dimensional semiconductor structures. In this study, the valence band structures of InAs/GaAs quantum ring and lens-shaped quantum dot are calculated with four-band model, in the framework of effective-mass envelope function theory. To determine the Hamiltonian matrix elements, this article develops the numerical Fourier transform method instead of the widely used analytical integral method. The valence band mixing is considered. The hole energy levels change dramatically with the geometrical parameters of the quantum ring and quantum dot. It is demonstrated that numerical Fourier transform method can be adopted in low-dimensional structures with any shape. The results of Fourier transform method are consistent with the ones of analytical integral in literature; and they are helpful for studying and fabricating optoelectronic devices.

Intersubband optical transitions in InAs/GaSb quantum wells

The effects of electron-hole hybridization, structural asymmetry with respect to spatial inversion, bulk asymmetry, and the interface Hamiltonian upon the optical absorption of linearly polarized light in broken-gap heterostructures are treated with the use of the eight-band Burt-Foreman envelope function theory and the self-consistent solution of the Schrodinger equation and the Poisson equation. The broken-gap heterostructures, specifically, the AlSb/InAs/GaSb/AlSb quantum wells, grown along the [001] direction offer promise for the fabrication of various devices. The anisotropy induced by the above-listed effects in the dispersion relations of size-quantization subbands and in optical matrix elements is established. The bulk asymmetry and the interface Hamiltonian modify the selection rules for intersubband transitions on the exposure of the structures to linearly polarized light. As a result, the initially forbidden spin-flip transitions are allowed. This brings about a large number of peaks in the dependence of the absorption coefficient on the photon energy, if the light polarization vector is directed along the axis of growth of the structure. If the light polarization vector is in the plane of the structure, the bulk asymmetry and the interface Hamiltonian induce strong longitudinal anisotropy of the absorption due to the hybridization of states with oppositely oriented spins. These effects are comprehensively studied for optical transitions involving hybridized electron-hole states in quantum wells grown on InAs.

Depolarization blueshift in intersubband transitions of triangular quantum wires

The depolarization effect (DE) in the intersubband transitions (ISBTs) of triangular cross-section quantum wires has been calculated in the framework of the effective-mass envelope-function theory and the self-consistent field approximation (Hartree approximation). Similar to quantum wells, the DE can bring an upward shift in ISBT. The shift quantities are affected significantly by apex angle but are insensitive to triangle size.

Electronic structures of GaAs/AlGaAs concentric double rings in applied electric and magnetic field

The electronic structures of GaAs/Al 0.35Ga 0.65As concentric double rings are calculated based on the effective mass envelope function theory, with and without the applied electric and magnetic field along the growth direction. The Hamiltonian matrix elements are determined through the Fourier transform method. As the heterostructure evolves from a single ring to the concentric double rings, our simulation is performed on the bound state energies of the electron and the hole. The results show that the energy levels undulate with the evolution of the ring. The applied magnetic field increases the ground state energies both of the electron and of the hole, as well as the transition energy between the first conduction subband and valence subband. However, the electric field decreases the electronic energies linearly.

Binding energy of ionized-donor-bound excitons in parabolic quantum-well wires in a magnetic field

The properties of ionized-donor-bound excitons (D+,X) in a parabolic quantum-well wire in the presence of a magnetic field are studied numerically in the framework of effective-mass envelope function theory. The binding energy of (D+,X) structures is calculated as a function of the oscillator length for different values of the magnetic field by using the one-dimensional effective potential model and the finite-difference method. The results show that the binding energy increases as the oscillator length decreases, and that it is also increased by enhancing the magnetic field. The binding energies of the complex for the two different dissociation processes are taken into account, and their behaviors are discussed in detail. The Haynes factor is found to increase rapidly with decreasing oscillator length in the case of strong parabolic potential confinement. In addition, the average interparticle distances and the probability density distributions are investigated for a given set of values of the oscillator lengths and the magnetic field.

Binding Energy and Spin-Orbit Splitting of a Hydrogenic Donor Impurity in AlGaN/GaN Triangle-Shaped Potential Quantum Well

In the framework of effective-mass envelope function theory, including the effect of Rashba spin-orbit coupling, the binding energyEband spin-orbit split energy Г of the ground state of a hydrogenic donor impurity in AlGaN/GaN triangle-shaped potential heterointerface are calculated. We find that with the electric field of the heterojunction increasing, (1) the effective width of quantum well decreases and (2) the binding energy increases monotonously, and in the mean time, (3) the spin-orbit split energy Г decreases drastically. (4) The maximum of Г is 1.22 meV when the electric field of heterointerface is 1 MV/cm.

Electronic States of a Shallow Hydrogenic Donor Impurity in Different Shaped Semiconductor Quantum Wells

The shallow hydrogenic donor impurity states in square, V-shaped, and parabolic quantum wells are studied in the framework of effective-mass envelope-function theory using the plane wave basis. The first four impurity energy levels and binding energy of the ground state are more easily calculated than with the variation method. The calculation results indicate that impurity energy levels decrease with the increase of the well width and decrease quickly when the well width is small. The binding energy of the ground state increases until it reaches a maximum value, and then decreases as the well width increases. The results are meaningful and can be widely applied in the design of various optoelectronic devices.

External electric field effect on the hydrogenic donor impurity in zinc-blende GaN/AlGaN cylindrical quantum dot

The binding energy of a hydrogenic donor impurity in a zinc-blende GaN/AlGaN cylindrical quantum dot (QD) is calculated in the framework of effective-mass envelope-function theory using the plane wave basis. It is shown that the donor binding energy is highly dependent on the impurity position and QD size. The external electric field induces an asymmetrical distribution of the donor binding energy with respect to the center of the QD. The maximum of the donor binding energy is shifted from the center of the QD. The degenerating energy levels for symmetrical positions with respect to the center of QD are also split. The splitting increases with the increase in QD height while the splitting increases up to a maximum and then decreases with the increase in QD radius. In the presence of the external electric field, the donor binding energy is insensitive to dot height when the impurity is located at the left side of the QD with large dot height. In addition, Stark shift dependence on hydrogenic impurity position is calculated.

Valence band structures of InAs/GaAs quantum rings using the Fourier transform method

The valence band structures of strained InAs/GaAs quantum rings are calculated, with the four-band k · p model, in the framework of effective-mass envelope function theory. When determining the Hamiltonian matrix elements, we develop the Fourier transform method instead of the widely used analytical integral method. Using Fourier transform, we have investigated the energy levels as functions of the geometrical parameters of the rings and compared our results with those obtained by the analytical integral method. The results show that the energy levels in the quantum rings change dramatically with the inner radius, outer radius, average radius, width, height of the ring and the distance between two adjacent rings. Our method can be adopted in low-dimensional structures with arbitrary shape. Our results are consistent with those in the literature and should be helpful for studying and fabricating optoelectronic devices.

Linear Rashba Model of a Hydrogenic Donor Impurity in GaAs/GaAlAs Quantum Wells

The Rashba spin-orbit splitting of a hydrogenic donor impurity in GaAs/GaAlAs quantum wells is investigated theoretically in the framework of effective-mass envelope function theory. The Rashba effect near the interface between GaAs and GaAlAs is assumed to be a linear relation with the distance from the quantum well side. We find that the splitting energy of the excited state is larger and less dependent on the position of the impurity than that of the ground state. Our results are useful for the application of Rashba spin-orbit coupling to photoelectric devices.

Optical absorption of polarized light in InAs/GaSb quantum wells

Using an eight-band k ⋅ p model Hamiltonian with the Burt–Foreman envelope function theory, we have investigated the optical absorption of both linearly and circularly polarized light, as well as related phenomena in InAs/GaSb broken-gap quantum wells grown along the [0 0 1] direction, with emphasis on the effects of electron–hole hybridization and the various symmetry-breaking mechanisms such as structural inversion asymmetry, bulk inversion asymmetry and interface Hamiltonian. The optical matrix elements exhibit unusual angular dependence in close connection with the spin-flip transitions which are originally forbidden. The spin split of the 2e subband results in two profound absorption peaks for the 1hh–2e transition for both linearly polarized and circularly polarized light. A large lateral optical anisotropy appears in the absorption coefficient of linearly polarized light, which can reach almost 100% with a reducing thickness of the quantum well. For the absorption of circularly polarized light, we found a large enhancement of electron spin polarization in the upper 2e subband, which was generally considered as forbidden if the polarization is along the direction perpendicular to the plane-of-light incidence.

External Electric Field Effect on Hydrogenic Donor Impurity in Zinc-Blende InGaN Quantum Dot

The binding energy of a hydrogenic donor impurity in zinc-blende (ZB) InGaN quantum dot (QD) is calculated in the framework of effective-mass envelope-function theory using the plane wave basis. It is shown that the donor binding energy is highly dependent on the impurity position, QD size and the external electric field. The symmetry of the electron probability distribution is broken and the maximum of the donor binding energy is shifted from the centre of QD in the presence of the external electric field. The degenerating energy levels for symmetrical positions with respect to the centre of QD are split. The splitting increases with the increase of QD height while the splitting increases up to a maximum value and then decreases with the increase of QD radius.

Electronic Energy Levels in an Asymmetric Quantum-Dots-in-a-Well Structure for Infrared Photodetectors

Theoretical calculation of electronic energy levels of an asymmetric InAs/InGaAs/GaAs quantum-dots-in-a-well (DWELL) structure for infrared photodetectors is performed in the framework of effective-mass envelope-function theory Our calculated results show that the electronic energy levels in quantum dots (QDs) increase when the asymmetry increases and the ground state energy increases faster than the excited state energies. Furthermore, the results also show that the electronic energy levels in QDs decrease as the size of QDs and the width of quantum well (QW) in the asymmetric DWELL structure increase. Additionally, the effects of asymmetry, the size of QDs and the width of QW on the response peak of asymmetry DWELL photodetectors are also discussed.

Plane wave methodology for single quantum dot electronic structure calculations

The development of the plane wave methodology for the calculation of the electronic structure of single quantum dots within the framework of multiband envelope function theory was presented. The methodology developed enables one to use a small embedding box, sufficient to eliminate electronic coupling, without introducing the artificial interaction with periodically replicated array of quantum dots caused by periodic boundary conditions. The appropriate formulas for Fourier transforms of strain tensor components on the embedding box that eliminate the strain field of the neighboring dots were derived. The expressions that enable the evaluation of Coulomb integrals in inverse space without the introduction of artificial electrostatic interactions with surrounding dots were presented. It was also shown how symmetry can be exploited to further reduce the computational effort in the case of quantum dots of symmetric shape. Numerical results illustrating the application of the methods to the calculation of single-particle states, as well as the configuration interaction calculation of exciton, biexciton, and negative trion states in InAs∕GaAs quantum dots were given.

Quantum dot properties in the multiband envelope-function approximation using boundary conditions based upon first-principles quantum calculations

A number of physical processes involving quantum dots depend critically upon the ``evanescent'' electron eigenstate wave function that extends outside of the material surface into the surrounding region. These processes include electron tunneling through quantum dots, as well as interactions between multiple quantum dot structures. In order to unambiguously determine these evanescent fields, appropriate boundary conditions have been developed to connect the electronic solutions interior to the semiconductor quantum dot to exterior vacuum solutions. In standard envelope function theory, the interior wave function consists of products of band edge and envelope functions, and both must be considered when matching to the external solution. While the envelope functions satisfy tractable equations, the band edge functions are generally not known. In this work, symmetry arguments in the spherically symmetric approximation are used in conjunction with the known qualitative behavior of bonding and antibonding orbitals to catalog the behavior of the band edge functions at the unit cell boundary. This physical approximation allows consolidation of the influence of the band edge functions to two simple surface parameters that are incorporated into the boundary conditions and are straightforwardly computed by using numerical first-principles quantum techniques. These new boundary conditions are employed to analyze an isolated spherically symmetric semiconductor quantum dot in vacuum within the analytical model of Sercel and Vahala [Phys. Rev. Lett. 65, 239 (1990); Phys. Rev. B 42, 3690 (1990)]. Results are obtained for quantum dots made of GaAs and InP, which are compared with ab initio calculations that have appeared in the literature.

Electronic structure and optical gain of wurtzite ZnO nanowires

The electronic structure and optical gain of wurtzite ZnO nanowires are investigated in the framework of effective-mass envelope-function theory. We found that as the elliptical aspect ratio e increases to be larger than a critical value, the hole ground states may change from optically dark to optically bright. The optical gain of ZnO nanowires increases as the hole density increases. For elliptical wire with large e, the y-polarized mode gain can be several thousand cm−1, while the x-polarized mode gain may be 26 times smaller than the former, so they can be used as ultraviolet linearly polarized lasers.

Effect of nonrelativistic interface Hamiltonian on optical transitions in broken-gap heterostructures

Using the Burt-Foreman envelope function theory and an eight-band k p model, we have extended our previous work on optical transitions in InAs/GaSb quantum wells grown along the [001] direction by ...

Spin-orbit splitting of a hydrogenic donor impurity in GaAs∕GaAlAs quantum wells

The electronic states of a hydrogenic donor impurity in GaAs∕GaAlAs quantum wells are investigated theoretically in the framework of effective-mass envelope function theory, including the effect of Rashba spin-orbit coupling. The splits of electron energy levels are calculated. The results show that (1) the split energy of the excited state is larger than that of the ground state; (2) the split energy peak appears as the GaAs well width increases from zero; and (3) the maximum split energy reaches about 1.6meV. Our results are useful for the application of Rashba spin-orbit coupling to photoelectric devices.

Thermoelectric properties of transverse transport in nanowire array structures

The electronic structures of nanowire-composite arrays are calculated theoretically in the framework of effective-mass envelope function theory，and various coefficients about electronic transport are obtained. At the same time，a closed-form expression based on boundary scattering theory for lattice thermal conductivity is presented. Then the thermoelectric properties of Si nanowire/Ge host material are investigated as function of the Fermi energy，wire diameter and separation between nanowire sidewalls. The results show that the ZT value of nanowire-composite can be significantly increased by carefully adjusting the correlative parameters of the structure.